# HG changeset patch # User wenzelm # Date 1475343021 -7200 # Node ID 4c4049e3bad8739446fc71b8a3f10437b28e6da3 # Parent 6f7db4f8df4c4495655bdc2f01354d4eb6566271 tuned; diff -r 6f7db4f8df4c -r 4c4049e3bad8 src/HOL/Finite_Set.thy --- a/src/HOL/Finite_Set.thy Sat Oct 01 19:29:48 2016 +0200 +++ b/src/HOL/Finite_Set.thy Sat Oct 01 19:30:21 2016 +0200 @@ -139,12 +139,12 @@ qed qed -lemma finite_conv_nat_seg_image: "finite A \ (\(n::nat) f. A = f ` {i::nat. i < n})" +lemma finite_conv_nat_seg_image: "finite A \ (\n f. A = f ` {i::nat. i < n})" by (blast intro: nat_seg_image_imp_finite dest: finite_imp_nat_seg_image_inj_on) lemma finite_imp_inj_to_nat_seg: assumes "finite A" - shows "\f n::nat. f ` A = {i. i < n} \ inj_on f A" + shows "\f n. f ` A = {i::nat. i < n} \ inj_on f A" proof - from finite_imp_nat_seg_image_inj_on [OF \finite A\] obtain f and n :: nat where bij: "bij_betw f {i. i